Moshe Kress

A multiple criteria decision model with ordinal preference data

Abstract This paper develops a model for aggregating ordinal preference ranking across multiple criteria. Criteria weights are developed as part of the optimization process. The model utilizes three levels of ordinal priorities: (1) preferences among alternatives on the basis of each criterion; (2) preferences among the criteria to reflect the importance of those criteria; and (3) preferences among the criteria which express the degree to which the respondent can clearly distinguish among the alternatives. The model is based upon a Data Envelopment Analysis structure which permits a flexible weighting mechanism for each alternative being ranked.

Characterizing an equitable allocation of shared costs: A DEA approach

Abstract In many applications to which DEA could be applied, there is often a fixed or common cost which is imposed on all decision making units. This would be the case, for example, for branches of a bank which can be accessed via the numerous automatic teller machines scattered throughout the country. A problem arises as to how this cost can be assigned in an equitable way to the various DMUs. In this paper we propose a DEA approach to obtain this cost allocation which is based on two principles: invariance and pareto-minimality. It is shown that the proposed method is a natural extension of the simple one-dimensional problem to the general multiple-input multiple-output case.

A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices

Abstract Ratio-scale matrices are commonly used as a vehicle to distinguish among competing alternatives or conflicting criteria. The issue of extracting weights out of such matrices has attracted increasing attention in recent years and resulted in the development of several scaling methods. This paper presents an attempt to evaluate some of the more known techniques in this area. The evaluation procedure includes random generation of a large number of representative matrices which are used to evaluate the various scaling methods according to the specified criteria. The performance of the different techniques is analyzed with respect to the proposed criteria and conclusions are drawn.

A general framework for distance-based consensus in ordinal ranking models

Abstract The problem of aggregating a set of ordinal rankings of n alternatives has given rise to a number of consensus models. Among the most common of these models are those due to Borda and Kendall, which amount to using average ranks, and the l1 and l2 distance models. A common criticism of these approaches is their use of ordinal rank position numbers directly as the values of being ranked at those levels. This paper presents a general framework for associating value or worth with ordinal ranks, and develops models for deriving a consensus based on this framework. It is shown that the lp distance models using this framework are equivalent to the conventional ordinal models for any p ⩾ 1. This observation can be seen as a form of validation of the practice of using ordinal data in a manner for which it was presumably not designed. In particular, it establishes the robustness of the simple Borda, Kendall and median ranking models.

Deriving weights from pairwise comparison ratio matrices: An axiomatic approach

Abstract This paper examines the problem of extracting object or attribute weights from a pairwise comparison ratio matrix. This problem is approached from the point of view of a distance measure on the space of all such matrices. A set of axioms is presented which such a distance measure should satisfy, and the uniqueness of the measure is proven. The problem of weight derivation is then shown to be equivalent to that of finding a totally transitive matrix which is a minimum distance from the given matrix. This problem reduces to a goal programming model. Finally, it is shown that the problem of weight derivation is related to that of ranking players in a round robin tournament. The space of all binary tournament matrices is proven to be isometric to a subset of the space of ratio matrices.

Optimal Allocation of Proposals to Reviewers to Facilitate Effective Ranking

Peer review of research proposals and articles is an essential element in research and development processes worldwide. Here we consider a problem that, to the best of our knowledge, has not been addressed until now: how to assign subsets of proposals to reviewers in scenarios where the reviewers supply their evaluations through ordinal ranking. The solution approach we propose for this assignment problem maximizes the number of proposal pairs that will be evaluated by one or more reviewers. This new approach should facilitate meaningful aggregation of partial rankings of subsets of proposals by multiple reviewers into a consensus ranking. We offer two ways to implement the approach: an integer-programming set-covering model and a heuristic procedure. The effectiveness and efficiency of the two models are tested through an extensive simulation experiment.

Prioritization models for frontier decision making units in DEA

Abstract Data Envelopment Analysis (DEA) has received significant attention in recent years as a tool for measuring the relative efficiency of each member of a set of Decision Making Units (DMUs). Typically, a relatively large proportion of the DMUs will be credited with an efficiency score of 1, with no clear means of discriminating among such units. In a number of applications, however, it may be necessary to select a ‘winning’ DMU from this set of frontier units. This paper examines various conditions that are imposed on the multipliers in a DEA analysis. In each case, an approach is suggested for breaking ties on the frontier.

A multiple-criteria composite index model for quantitative and qualitative data

Abstract This paper provides a framework for evaluating a set of alternatives relative to a combination of ordinal and cardinal criteria. The proposed model creates a mixed criteria composite index for each alternative being considered, thereby providing a vehicle for prioritizing the alternative set. Applications are presented involving the ranking of capital construction projects in a hydroelectric company, and the prioritization of highway rehabilitation and construction initiatives. The status of implementation of a software package for the model is discussed. Shortcomings and concerns are examined.

Approximate articulation of preference and priority derivation — a comment

Abstract In a recent paper by A. Arbel (1989) the standard Analytic Hierarchy Process (AHP) model is extended to the case where preference strength is expressed in terms of a range of scale values rather than a single value. While this extension holds and is natural for the consistent case, it is shown that the proposed solution for the (more common) inconsistent case is erroneous.

Why Defeating Insurgencies Is Hard: The Effect of Intelligence in Counterinsurgency Operations---A Best-Case Scenario

In insurgency situations, the government-organized force is confronted by a small guerrilla group that is dispersed in the general population with no or a very small signature. Effective counterinsurgency operations require good intelligence. Absent intelligence, not only might the insurgents escape unharmed and continue their violent actions, but collateral damage caused to the general population from poor targeting may generate adverse response against the government and create popular support for the insurgents, which may result in higher recruitment to the insurgency. We model the dynamic relations among intelligence, collateral casualties in the population, attrition, recruitment to the insurgency, and reinforcement to the government force. Even under best-case assumptions, we show that the government cannot totally eradicate the insurgency by force. The best it can do is contain it at a certain fixed level.